The version of the application I analyzed stores its logs under 'userprofile\\Application Data\\Free Download Manager'. It uses a number of files to handle different logs and track various in-process tasks. Here's a list of the files I found there:

dlmgrsi.sav - This is actually a short executable of some description. Not sure what it's for.

downloads.his.sav - Log file using the following format: Starts with the null-terminated header "FDM Downloads History". Then 8 bytes of unknown data, followed by a list of records as follows,

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